In this paper, we propose a new receiver for detecting signals in large-scale Spatially Multiplexed (SP) Multiple-Input-Multiple-Output (MIMO) systems that may have fewer receive antennas than transmitted symbols (overloaded case). Relying on the idea of Finite-Alphabet Sparse (FAS) detection, we formulate the Maximum Likelihood (ML) criterion as a Difference-of-Convex (DC) programming problem that can be simply and efficiently solved using the Concave-Convex Procedure (CCP) technique. Since, the considered problem is non-convex, we theoretically discuss the behavior of the derived algorithm. Numerical experiments confirm the superiority of the proposed detection scheme, when compared with recent detection methods based on convex optimization, in a variety of large-scale MIMO transmission scenarios including the overloaded case.